We show that an algebra over a cyclic operad supplied with an additional linear algebra datum called Hodge decomposition admits a minimal model whose structure maps are given in terms of summation over trees. This minimal model is unique up to homotopy.

This is the author's final draft of the paper published online on 25 March 2009 in Letters in Mathematical Physics. The original publication is available at www.springerlink.com. Doi: 10.1007/s11005-009-0314-7